Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

TL;DR

This paper challenges the emphasis on degree distributions in network controllability, highlighting the importance of nodal dynamics and other factors over structural controllability predictions.

Contribution

It argues that nodal dynamics, not degree distributions, primarily determine the controllability of complex networks, shifting focus from structural properties to system-specific dynamics.

Findings

Single control input suffices for most real-world networks

Structural controllability is less informative than nodal dynamics

Almost uncontrollable and unobservable states are more critical issues

Abstract

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.